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Relativistic Velocity and Kinetic Energy

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Take the mass of a proton to be 1GeV (=1000MeV). Find the velocity (beta) of a proton whose kinetic energy is:

100 MeV
2 GeV
10 GeV
100 GeV

According to Newtonian theory, the kinetic energy (mv^2/2) of a particle is c is equal to mc^2/2, which we now recognize as half of its rest energy. What is the actual (relativistic) velocity of a particle whose kinetic energy is equal to half its rest energy?

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The solution finds the velocity of a proton whose has a given kinetic energy. The solution examines Newtonian theory.

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